Question

The magnitude of the resultant of two forces each having magnitude $F_0$ and angle between them is ${120}^{\circ },$ is $x{F}_0.$ Then $x$ is

• A. 1
• B. 2
• C. 3
• D. $\sqrt{2}$

Answer 1

The correct option is A 1

$F_{resultant}^2=F_o^2+F_o^2+2F_o^2\cos \theta$
$=2F_o^2(1+\cos \theta )$
$=2F_o^2(1+2{\cos }^2\frac{\theta }{2}-1)$
$=2F_o^2\times 2{\cos }^2\frac{\theta }{2}$
$F_{resultant}=|2F_{o}cos\frac{\theta }{2}|$
$=|2F_{o}cos\frac{{120}^{\circ }}{2}|$
$=F_o$